34=5x*2+5x2

Solution for 34=5x*2+5x2 equation:

34=5x*2+5x^2

We move all terms to the left:

34-(5x*2+5x^2)=0

We get rid of parentheses

-5x^2-5x*2+34=0

Wy multiply elements

-5x^2-10x+34=0

a = -5; b = -10; c = +34;
Δ = b2-4ac
Δ = -102-4·(-5)·34
Δ = 780
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{195}}{2*-5}=\frac{10-2\sqrt{195}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{195}}{2*-5}=\frac{10+2\sqrt{195}}{-10}
$